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The loads induced on the spacecraft orbiting the Earth by the deploying elastic arm are investigated. The coupled equations of motion of the arm with the vehicle orbital mechanics are used to describe the 3D dynamic behavior of the flexible-appendage and the related disturbing loads induced on the spacecraft. To this end, an equivalent dynamical system is derived for the arm by applying an attached Non-Newtonian Reference Frame which is subjected to the orbital motion and geocentric pointing maneuver of the spacecraft. With the help of the Assumed Modes Method, the behavior of the arm attached to the spacecraft in Keplerian orbits is studied. The results show that deploying the arm in some specific directions relative to the orbital plane leads to serious coupling between two lateral displacements. In addition, the effects of specific orbital parameters on arm responses and resulting induced loads are studied for the cases of "True Anomaly of spacecraft at deployment time, and Eccentricity of elliptical orbits". The prediction of disturbing loads induced on spacecraft helps design the robust attitude control system. Further, the positioning accuracy of the payloads (installed on the arm-tip) can be estimated by employing the obtained arm responses in the orbital motion, which enables us to determine the undesirable motions and predict any required control system for the arm.

Problems related to the three-dimensional (3D) dynamics of the deploying flexible arms subjected to base angular motions are studied with simulated tip payloads and actual deployment trajectories. To facilitate the solution, an equivalent dynamical system is developed by introducing the inertial reaction forces on the arm, while the equations of motion are derived in the non-Newtonian reference frame attached to the arm. The dynamic behavior of the arm is investigated both by the finite element and assumed Modes methods for the purpose of verification. This study reveals that base angular motions lead to considerable couplings between the two lateral displacements and axial motions. Meanwhile, the induced loadings on the flexible arm due to the base angular motions are obtained, which are useful for the design of more efficient arms. Furthermore, one may use the resulting arm–tip position envelop to predict the antenna positioning accuracy, which paves the way for possible control systems to limit undesirable motions.

Modal coupling is an important characteristic of most nonlinear dynamic systems. Although the existence of modal coupling can make the dynamic responses of a system quite complicated, it can be utilized to provide potential solutions to regulate nonlinear vibration. In this paper, the mechanism of modal coupling is used as a means to suppress vibration of a flexible arm undergoing joint motion. A secondary oscillatory system is attached to the flexible arm to generate appropriate modal coupling. Via this nonlinear coupling, internal resonance can be successfully induced and used to transfer vibration energy from the flexible arm to the vibration absorber. Moreover, the damping enhancement effect is studied, which is found to help suppressing vibrations. The feasibility of the idea presented herein has been demonstrated in the numerical simulations.

The space flexible arm has the characteristics of large flexibility and size, and external excitation will cause harmful vibration. In this paper, the dynamic response of flexible arms is analyzed, and the vibration control is studied when nonlinear factors are considered. First, the vibration equation is established according to the Hamilton’s principle, and the generalized force is derived by using rod model and beam model, respectively. Then the Runge–Kutta method is used to solve the vibration equation, and the dynamic response is obtained. Finally, the PD and fuzzy control simulations of three arms are established, and the dead zone and saturation nonlinearities are applied in the programs. The numerical results show that the external force causes significant response, and the vibration control method is effective. Besides, in order to achieve vibration control effect, it is necessary to reduce the dead zone nonlinear range.

In this article, A feedback control law for controlling the tip position of a flexible arm is proposed and evaluated. The objective of this research is to design a sensing antenna, a robot based on a single - link flexible arm which will enable us to locate a contact position with an object in order to detect the precise shape of that object. In a previous work, a nonlinear dynamic model was derived through the Lagrangian formulation where elastic characterics of the arm were modeled using the Euler - Bernoulli beam theory. Based on this model, an effective nonlinear controller was developed. Simulation results are given to show the controller's effectiveness.